Finite Group Databasebeta

← C2×#20246724 #26384970

Subgroups — C2×#20246724 #26384970

Order 12032.

5718 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625354C211yesmaximal, characteristic
2C22×#13094009C212yesmaximal, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246724C2116yesmaximal, direct product factor
5C2×#15689042C211yesmaximal, characteristic, complemented
6C2×#15689041C211yesmaximal, characteristic, complemented
7C2×#15689040C211yesmaximal, characteristic, complemented
8C2×#15689001C212yesmaximal, complemented
9C2×#15688997C212yesmaximal, complemented
10C2×#15688994C212yesmaximal, complemented
11C2×#15688985C211yesmaximal, characteristic, complemented
12C2×C47×#395C211yesmaximal, characteristic, complemented
13C22×#10625354—216no—
14C22×#10625354—28no—
15C22×#10625354C2218yes—
16C23×D188C2211yescharacteristic
17C23×D188C2212yes—
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2212yes—
21C23×C4×D47C2211yescharacteristic
22C2×#13094009—216no—
23C2×#13094009C22116yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2212yes—
28C2×C4⋊C4×D47—28no—
29C2×C4⋊C4×D47C2218yescomplemented
30C22×(C2×D47)⋊C4C2212yes—
31C22×(C2×D47)⋊C4C2212yes—
32C22×(C2×D47)⋊C4C2212yes—
33C22×(C2×D47)⋊C4C2212yes—
34C22×(C2×D47)⋊C4C2212yes—
35#15689042C2218yescomplemented
36#15689041C2218yescomplemented
37#15689040C2218yescomplemented
38#15689001C22116yescomplemented
39#15688997C22116yescomplemented
40#15688994C22116yescomplemented
41#15688985C2218yescomplemented
42C2×C47⋊#95C2212yes—
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2212yes—
45C23×Q8×C47C2211yescharacteristic
46C22×C4⋊C4×C47C2211yescharacteristic
47C22×C4⋊C4×C47C2212yes—
48C47×#395C2218yescomplemented
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2212yes—
51C24×D47C2312yes—
52C24×D47C2311yescharacteristic
53C2×#10625354—2128no—
54C2×#10625354—264no—
55C2×#10625354—232no—
56C22×D188—28no—
57C22×D188—28no—
58C22×D188—28no—
59C22×D188—24no—
60C22×D188D4116yes—
61C22×D188C2314yes—
62C22×D188C2318yes—
63C23×Dic47C2312yes—
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C22×C4×D47—24no—
68C22×C4×D47—28no—
69C22×C4×D47—28no—
70C22×C4×D47—28no—
71C22×C4×D47—24no—
72C22×C4×D47—28no—
73C22×C4×D47—24no—
74C22×C4×D47—24no—
75C22×C4×D47—28no—
76C22×C4×D47D418yes—
77C22×C4×D47C2318yes—
78C22×C4×D47C2314yes—
79C22×C4×D47C2314yes—
80C22×C4×D47C2314yes—
81#13094009—264no—
82C2×C4⋊Dic47—24no—
83C2×C4⋊Dic47C2314yes—
84C2×Dic47⋊C4—24no—
85C2×Dic47⋊C4—28no—
86C2×Dic47⋊C4—24no—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2318yes—
89C2×Dic47⋊C4C2314yes—
90C4⋊C4×D47—232no—
91C2×(C2×D47)⋊C4—28no—
92C2×(C2×D47)⋊C4—28no—
93C2×(C2×D47)⋊C4—28no—
94C2×(C2×D47)⋊C4—28no—
95C2×(C2×D47)⋊C4—28no—
96C2×(C2×D47)⋊C4C2318yes—
97C2×(C2×D47)⋊C4C2318yes—
98C2×(C2×D47)⋊C4C2318yes—
99C2×(C2×D47)⋊C4C2318yes—
100C2×(C2×D47)⋊C4C2318yes—
101C47⋊#95C2318yes—
102C47⋊#95C2314yes—
103C47⋊#95C2318yes—
104C22×Q8×C47—28no—
105C22×Q8×C47—24no—
106C22×Q8×C47C2314yes—
107C23×C4×C47C2312yes—
108C23×C4×C47C2311yescharacteristic
109C23×C4×C47C2312yes—
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47—24no—
113C2×C4⋊C4×C47—28no—
114C2×C4⋊C4×C47C2318yes—
115C2×C4⋊C4×C47C2314yes—
116#95×C47C2314yes—
117#95×C47C2318yes—
118C24×C47C2411yescharacteristic
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—24no—
122C23×D47—24no—
123C23×D47—24no—
124C23×D47—24no—
125C23×D47—24no—
126C23×D47—24no—
127C23×D47—24no—
128C23×D47C2×D418yes—
129C23×D47C2×D418yes—
130C23×D47C2×D414yes—
131C23×D47C2414yes—
132C23×D47C2412yes—
133C2×Q8×C47—232no—
134C2×Q8×C47—216no—
135C2×Q8×C47—28no—
136C22×C4×C47—22no—
137C22×C4×C47—24no—
138C22×C4×C47—24no—
139C22×C4×C47—24no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—24no—
143C22×C4×C47—22no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47C2×D418yes—
147C22×C4×C47C2×D414yes—
148C22×C4×C47#4114yescomplemented
149C22×C4×C47C2412yes—
150C22×C4×C47C2414yes—
151C22×C4×C47C2414yes—
152C22×C4×C47C2412yes—
153C22×C4×C47C2412yes—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47—22no—
157C22×Dic47—24no—
158C22×Dic47—24no—
159C22×Dic47—22no—
160C22×Dic47—24no—
161C22×Dic47—24no—
162C22×Dic47C2×D414yes—
163C22×Dic47#4114yescomplemented
164C22×Dic47C2414yes—
165C22×Dic47C2412yes—
166C22×Dic47C2412yes—
167C22×Dic47C2412yes—
168#10625354—2256no—
169C2×D188—232no—
170C2×D188—264no—
171C2×D188—216no—
172C2×D188—216no—
173C2×D188—216no—
174C2×D188—28no—
175C2×D188C2×D4132yes—
176C2×C4×D47—232no—
177C2×C4×D47—264no—
178C2×C4×D47—232no—
179C2×C4×D47—28no—
180C2×C4×D47—216no—
181C2×C4×D47—216no—
182C2×C4×D47—216no—
183C2×C4×D47—28no—
184C2×C4×D47—216no—
185C2×C4×D47—28no—
186C2×C4×D47—28no—
187C2×C4×D47—216no—
188C2×C4×D47—416no—
189C2×C4×D47C2×D4116yes—
190C4⋊C4×C47—28no—
191C4⋊C4×C47—216no—
192(C2×D47)⋊C4—216no—
193(C2×D47)⋊C4—216no—
194(C2×D47)⋊C4—216no—
195(C2×D47)⋊C4—216no—
196(C2×D47)⋊C4—216no—
197C4⋊Dic47—28no—
198Dic47⋊C4—28no—
199Dic47⋊C4—216no—
200Dic47⋊C4—28no—
201C23×C47C22×D412yes—
202C23×C47C22×D414yes—
203C23×C47C2×#4112yes—
204C23×C47C2×#4112yes—
205C23×C472−1+414yes—
206C23×C47C2511yescharacteristic
207C22×D47—28no—
208C22×D47—28no—
209C22×D47—216no—
210C22×D47—216no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—24no—
214C22×D47—216no—
215C22×D47—216no—
216C22×D47—216no—
217C22×D47—24no—
218C22×D47—24no—
219C22×D47—24no—
220C22×D47—24no—
221C22×D47—24no—
222C22×D47—24no—
223C22×D47—48no—
224C22×D47—48no—
225C22×D47—48no—
226C22×D47—48no—
227C22×D47#120116yes—
228C22×D47C22×D418yes—
229C22×D47C22×D418yes—
230C22×D47C22×D414yes—
231Q8×C47—232no—
232C2×C4×C47—216no—
233C2×C4×C47—28no—
234C2×C4×C47—28no—
235C2×C4×C47—22no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—44no—
246C2×C4×C47—48no—
247C2×C4×C47C22×D418yes—
248C2×C4×C47C22×D414yes—
249C2×C4×C47C2×#4114yescomplemented
250C2×Dic47—28no—
251C2×Dic47—28no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—44no—
261C2×Dic47—48no—
262C2×Dic47C22×D414yes—
263C2×Dic47C2×#4114yescomplemented
264D188—232no—
265D188—264no—
266C4×D47—232no—
267C4×D47—264no—
268C4×D47—232no—
269C4×D47—416no—
270C2×#2406—471nomaximal, Sylow
271C22×C47C2×#12014yes—
272C22×C47#52514yes—
273C22×C47#53614yes—
274C22×C47#54718yes—
275C22×C47#54718yes—
276C22×C47C23×D411yescharacteristic
277C22×C47C23×D412yes—
278C22×C47C22×#4111yescharacteristic
279C22×C47C22×#4111yescharacteristic
280C22×C47C2×2−1+412yes—
281C2×D47—232no—
282C2×D47—24no—
283C2×D47—24no—
284C2×D47—28no—
285C2×D47—28no—
286C2×D47—28no—
287C2×D47—28no—
288C2×D47—28no—
289C2×D47—432no—
290C2×D47—44no—
291C2×D47—44no—
292C2×D47—44no—
293C2×D47—44no—
294C2×D47C2×#12018yes—
295C4×C47—28no—
296C4×C47—24no—
297C4×C47—24no—
298C4×C47—42no—
299C4×C47—44no—
300Dic47—24no—
301Dic47—24no—
302Dic47—42no—
303Dic47—44no—
304C23×#41—471no—
305C22×#123—472no—
306C23×C4⋊C4—471no—
307#2406—4716no—
308C2×#395—471no—
309C2×#395D4711yescharacteristic, complemented
310C2×#394—471no—
311C2×#394—471no—
312C2×#386—472no—
313C2×#385—472no—
314C2×#385—472no—
315C2×#381—471no—
316C2×C47#240618yescomplemented
317C2×C47C22×#12011yescharacteristic
318C2×C47C2×#52511yescharacteristic
319C2×C47C2×#53611yescharacteristic
320C2×C47C2×#54712yes—
321C2×C47C2×#54712yes—
322D47—28no—
323D47—48no—
324C22×#41—478no—
325C22×#41—948no—
326C22×#41—9416no—
327C23×Q8C2×D4711yescharacteristic
328C23×D4—472no—
329C23×D4—471no—
330C24×C4—471no—
331C24×C4—472no—
332C24×C4—471no—
333C24×C4—471no—
334C2×#123—4716no—
335C2×#123—9416no—
336C22×C4⋊C4—471no—
337C22×C4⋊C4—472no—
338C22×C4⋊C4—471no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4—478no—
341C22×C4⋊C4—948no—
342C22×C4⋊C4C2×D4711yescharacteristic
343C22×C4⋊C4C2×D4712yes—
344C22×C22⋊C4—472no—
345C22×C22⋊C4—472no—
346C22×C22⋊C4—472no—
347C22×C22⋊C4—472no—
348C22×C22⋊C4—472no—
349#395—478no—
350#395C2×D4718yescomplemented
351#394—478no—
352#394—478no—
353#386—4716no—
354#385—4716no—
355#385—4716no—
356#381—478no—
357C2×#95—471no—
358C2×#95—472no—
359C2×#95—472no—
360C2×#95C2×D4711yescharacteristic
361C2×#95C2×D4712yes—
362C47C2×#240611yescharacteristic, complemented, Sylow
363C25—471no—
364C25—472no—
365C2×#41—9432no—
366C2×#41—9464no—
367C2×#41—94128no—
368C22×Q8—24no—
369C22×Q8—28no—
370C22×Q8C22×D4714yes—
371C22×D4—4716no—
372C22×D4—478no—
373C22×D4—474no—
374C22×D4—948no—
375C22×D4—948no—
376C22×D4—948no—
377C22×D4—944no—
378C23×C4—471no—
379C23×C4—471no—
380C23×C4—478no—
381C23×C4—474no—
382C23×C4—472no—
383C23×C4—471no—
384C23×C4—474no—
385C23×C4—474no—
386C23×C4—478no—
387C23×C4—948no—
388C23×C4—944no—
389C23×C4—944no—
390C23×C4—948no—
391C23×C4—948no—
392C23×C4—944no—
393C23×C4—948no—
394C23×C4—948no—
395C23×C4—944no—
396C23×C4C22×D4712yes—
397C23×C4C22×D4711yescharacteristic
398C23×C4C22×D4711yescharacteristic
399C23×C4C22×D4712yes—
400C23×C4C22×D4711yescharacteristic
401#123—9464no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—474no—
405C2×C4⋊C4—474no—
406C2×C4⋊C4—474no—
407C2×C4⋊C4—478no—
408C2×C4⋊C4—9432no—
409C2×C4⋊C4—944no—
410C2×C4⋊C4—944no—
411C2×C4⋊C4—944no—
412C2×C4⋊C4—948no—
413C2×C4⋊C4C22×D4714yes—
414C2×C4⋊C4C22×D4718yes—
415C2×C22⋊C4—478no—
416C2×C22⋊C4—478no—
417C2×C22⋊C4—478no—
418C2×C22⋊C4—478no—
419C2×C22⋊C4—478no—
420C2×C22⋊C4—948no—
421C2×C22⋊C4—948no—
422C2×C22⋊C4—948no—
423C2×C22⋊C4—948no—
424C2×C22⋊C4—948no—
425#95—478no—
426#95—474no—
427#95—478no—
428#95C22×D4714yes—
429#95C22×D4718yes—
430C24—478no—
431C24—474no—
432C24—472no—
433C24—478no—
434C24—474no—
435C24—942no—
436C24—942no—
437C24—944no—
438C24—944no—
439C24—944no—
440C24—944no—
441C24—944no—
442C24—944no—
443C24—944no—
444C24C23×D4711yescharacteristic
445#41—94256no—
446C2×Q8—232no—
447C2×Q8—28no—
448C2×Q8—216no—
449C2×D4—4732no—
450C2×D4—9464no—
451C2×D4—9416no—
452C2×D4—9416no—
453C2×D4—9416no—
454C2×D4—9432no—
455C2×D4—948no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—474no—
467C22×C4—474no—
468C22×C4—472no—
469C22×C4—472no—
470C22×C4—4716no—
471C22×C4—474no—
472C22×C4—472no—
473C22×C4—948no—
474C22×C4—9416no—
475C22×C4—948no—
476C22×C4—9432no—
477C22×C4—9416no—
478C22×C4—9416no—
479C22×C4—9432no—
480C22×C4—9464no—
481C22×C4—948no—
482C22×C4—9416no—
483C22×C4—942no—
484C22×C4—944no—
485C22×C4—942no—
486C22×C4—9416no—
487C22×C4—948no—
488C22×C4—944no—
489C22×C4—944no—
490C22×C4—942no—
491C22×C4—944no—
492C22×C4—944no—
493C22×C4—18816no—
494C22×C4D4×D4714yes—
495C22×C4D4×D4718yes—
496C22×C4#1062535414yescomplemented
497C22×C4C23×D4714yes—
498C22×C4C23×D4712yes—
499C22×C4C23×D4712yes—
500C22×C4C23×D4714yes—
501C22×C4C23×D4712yes—
502C4⋊C4—28no—
503C4⋊C4—216no—
504C4⋊C4—948no—
505C4⋊C4—948no—
506C4⋊C4—948no—
507C4⋊C4—9416no—
508C22⋊C4—9416no—
509C22⋊C4—9416no—
510C22⋊C4—9416no—
511C22⋊C4—9416no—
512C22⋊C4—9416no—
513C23—4716no—
514C23—478no—
515C23—474no—
516C23—478no—
517C23—9416no—
518C23—9416no—
519C23—948no—
520C23—942no—
521C23—942no—
522C23—948no—
523C23—944no—
524C23—9416no—
525C23—9416no—
526C23—9416no—
527C23—944no—
528C23—944no—
529C23—944no—
530C23—944no—
531C23—944no—
532C23—944no—
533C23—1888no—
534C23—1888no—
535C23—1888no—
536C23—1888no—
537C23C2×D4×D4714yes—
538C23C2×D4×D4712yes—
539C23#41×D4712yes—
540C23C2×#1062535412yes—
541C23#1309407214yes—
542C23C24×D4711yescharacteristic
543Q8—232no—
544D4—9464no—
545D4—9432no—
546C2×C4—28no—
547C2×C4—216no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—474no—
562C2×C4—474no—
563C2×C4—9432no—
564C2×C4—9432no—
565C2×C4—9464no—
566C2×C4—948no—
567C2×C4—948no—
568C2×C4—942no—
569C2×C4—944no—
570C2×C4—942no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—942no—
574C2×C4—944no—
575C2×C4—944no—
576C2×C4—18816no—
577C2×C4—1888no—
578C2×C4—1884no—
579C2×C4C2×D4×D4714yes—
580C2×C4C2×D4×D4718yes—
581C2×C4C2×#1062535414yescomplemented
582C22—478no—
583C22—948no—
584C22—948no—
585C22—944no—
586C22—944no—
587C22—9432no—
588C22—948no—
589C22—948no—
590C22—948no—
591C22—1884no—
592C22—1884no—
593C22—1884no—
594C22—1884no—
595C22—18832no—
596C22#120×D4714yes—
597C22#1568963614yes—
598C22#1568969814yes—
599C22#1568977518yes—
600C22#1568977618yes—
601C22C22×D4×D4712yes—
602C22C22×D4×D4711yescharacteristic
603C22C2×#41×D4711yescharacteristic
604C22C22×#1062535411yescharacteristic
605C22C2×#1309407212yes—
606C4—24no—
607C4—28no—
608C4—24no—
609C4—44no—
610C4—42no—
611C4—944no—
612C4—944no—
613C4—1884no—
614C4—1882no—
615C2—948no—
616C2—1888no—
617C2#2024672418yesdirect product factor
618C2C2×#120×D4711yescharacteristic
619C2C2×#1568963611yescharacteristic
620C2C2×#1568969811yescharacteristic
621C2C2×#1568977512yes—
622C2C2×#1568977612yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#395C2
socleC24×C47C24
prime radicalC23×#10625354C2
hypercenterC2×#395D47
hypocenterC47C2×#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#13094009C2semidirect
3. C22×C4⋊C4×D47C2semidirect
4. #20246724C2direct (N × H)
5. C2×#15689042C2semidirect
6. C2×#15689041C2semidirect
7. C2×#15689040C2semidirect
8. C2×#15689001C2semidirect
9. C2×#15688997C2semidirect
10. C2×#15688994C2semidirect
11. C2×#15688985C2semidirect
12. C2×C47×#395C2semidirect
23. C2×#13094009C22semidirect
29. C2×C4⋊C4×D47C22semidirect
35. #15689042C22semidirect
36. #15689041C22semidirect
37. #15689040C22semidirect
38. #15689001C22semidirect
39. #15688997C22semidirect
40. #15688994C22semidirect
41. #15688985C22semidirect
48. C47×#395C22semidirect
148. C22×C4×C47#41semidirect
163. C22×Dic47#41semidirect
249. C2×C4×C47C2×#41semidirect
263. C2×Dic47C2×#41semidirect
309. C2×#395D47semidirect
316. C2×C47#2406semidirect
350. #395C2×D47semidirect
362. C47C2×#2406semidirect
496. C22×C4#10625354semidirect
581. C2×C4C2×#10625354semidirect
617. C2#20246724direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#106253542
C22×#130940092
C22×C4⋊C4×D472
#202467242
C2×#156890422
C2×#156890412
C2×#156890402
C2×#156890012
C2×#156889972
C2×#156889942
C2×#156889852
C2×C47×#3952
C2×#240647